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NCERT Exemplar Solutions Class 9 Science Solutions for Gravitation - Exercise in Chapter 10 - Gravitation

Question 25 Gravitation - Exercise

Two objects of masses m1 and m2 have the same size are dropped simultaneously from heights h1 and h2 respectively. Find out the ratio of time they would take in reaching the ground. Will this ratio remain the same if

(i) one of the objects is hollow and the other one is solid and

(ii) both of them are hollow, size remaining the same in each case. Give reason.

Answer:

h1 = 12 gt21

h2 = 12gt22

as x = ot1t2 2 = √h1/h2

As the acceleration remains the same, the ratio between two objects remains the same. In this case, acceleration does not depend upon mass and size.

Video transcript
"hello everyone welcome to leader learning i am good preet your science tutor today's question is two objects of masses m1 and m2 have the same size are dropped simultaneously from the heights h1 and h2 respectively find out the ratio of time they would take in reaching the ground will this ratio remain same if first one of the object is hollow and the other one is solid second both of them are hollow size remaining the same in each case give reasons so here in the question two objects have been given but they are of same size and drop from the height h1 and h2 you have to calculate the ratio of time they would take in reaching the ground so let's start our answer see here we'll apply the equation of motion that is second equation of motion h is equals to u t plus half gt square this we will apply here for finding out the ratio of time since the initial velocities are zero here okay because it is under the gravity so u will be equals to zero okay so the ratio equation will be h is equals to half of gt square now we'll apply this equation for both the masses for m1 and for m2 okay m1 and h1 height and for m2 and h2 height so here h1 will be equals to half of g t1 square and this will h2 will be equals to half of g t2 square so this equations you will get now for the ratio you will compare the formulas okay we need t1 and t2 so we'll write t1 square upon 2 square is equals to 2 h 1 upon g divided by 2 h 2 upon g g will be cancelled by g this and 2 we cancel and you will get the ratio as t 1 upon t 2 is equals to under root of h 1 upon under root of h2 okay so you will get the ratio t1 is 2 t2 will be under root h1 is to under root h2 this will be the ratio of time now they have been asking that two situations have been given in one of the object is hollow and the other one is solid and in second situation both of them are hollow but in both the cases one and two size remains the same so due to all this the conditions given acceleration due to gravity is same in both the cases so the ratio will also be same because acceleration due to gravity it does not depend on mass and size of the objects clear for more such videos please subscribe leaderlearning and for any doubts drop a comment thank you"
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